Properties

Label 8041.2.a.h.1.1
Level $8041$
Weight $2$
Character 8041.1
Self dual yes
Analytic conductor $64.208$
Analytic rank $1$
Dimension $74$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8041,2,Mod(1,8041)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8041.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8041.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(74\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 8041.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.77959 q^{2} -0.489198 q^{3} +5.72614 q^{4} -0.717152 q^{5} +1.35977 q^{6} -1.78399 q^{7} -10.3571 q^{8} -2.76069 q^{9} +O(q^{10})\) \(q-2.77959 q^{2} -0.489198 q^{3} +5.72614 q^{4} -0.717152 q^{5} +1.35977 q^{6} -1.78399 q^{7} -10.3571 q^{8} -2.76069 q^{9} +1.99339 q^{10} -1.00000 q^{11} -2.80122 q^{12} -2.65369 q^{13} +4.95875 q^{14} +0.350829 q^{15} +17.3364 q^{16} -1.00000 q^{17} +7.67358 q^{18} -1.91939 q^{19} -4.10651 q^{20} +0.872723 q^{21} +2.77959 q^{22} +2.92463 q^{23} +5.06669 q^{24} -4.48569 q^{25} +7.37616 q^{26} +2.81812 q^{27} -10.2153 q^{28} +3.37416 q^{29} -0.975163 q^{30} -2.56007 q^{31} -27.4737 q^{32} +0.489198 q^{33} +2.77959 q^{34} +1.27939 q^{35} -15.8081 q^{36} +11.2450 q^{37} +5.33513 q^{38} +1.29818 q^{39} +7.42764 q^{40} +4.76123 q^{41} -2.42581 q^{42} -1.00000 q^{43} -5.72614 q^{44} +1.97983 q^{45} -8.12929 q^{46} -0.457282 q^{47} -8.48091 q^{48} -3.81739 q^{49} +12.4684 q^{50} +0.489198 q^{51} -15.1954 q^{52} -5.27651 q^{53} -7.83322 q^{54} +0.717152 q^{55} +18.4770 q^{56} +0.938964 q^{57} -9.37878 q^{58} -1.26303 q^{59} +2.00890 q^{60} -13.8801 q^{61} +7.11595 q^{62} +4.92502 q^{63} +41.6931 q^{64} +1.90309 q^{65} -1.35977 q^{66} +13.3080 q^{67} -5.72614 q^{68} -1.43073 q^{69} -3.55618 q^{70} -0.440272 q^{71} +28.5928 q^{72} +12.3438 q^{73} -31.2566 q^{74} +2.19439 q^{75} -10.9907 q^{76} +1.78399 q^{77} -3.60841 q^{78} +14.4491 q^{79} -12.4328 q^{80} +6.90344 q^{81} -13.2343 q^{82} -2.65016 q^{83} +4.99733 q^{84} +0.717152 q^{85} +2.77959 q^{86} -1.65063 q^{87} +10.3571 q^{88} -16.2884 q^{89} -5.50312 q^{90} +4.73414 q^{91} +16.7469 q^{92} +1.25238 q^{93} +1.27106 q^{94} +1.37650 q^{95} +13.4401 q^{96} +18.0088 q^{97} +10.6108 q^{98} +2.76069 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77959 −1.96547 −0.982734 0.185022i \(-0.940764\pi\)
−0.982734 + 0.185022i \(0.940764\pi\)
\(3\) −0.489198 −0.282439 −0.141219 0.989978i \(-0.545102\pi\)
−0.141219 + 0.989978i \(0.545102\pi\)
\(4\) 5.72614 2.86307
\(5\) −0.717152 −0.320720 −0.160360 0.987059i \(-0.551266\pi\)
−0.160360 + 0.987059i \(0.551266\pi\)
\(6\) 1.35977 0.555124
\(7\) −1.78399 −0.674283 −0.337142 0.941454i \(-0.609460\pi\)
−0.337142 + 0.941454i \(0.609460\pi\)
\(8\) −10.3571 −3.66180
\(9\) −2.76069 −0.920228
\(10\) 1.99339 0.630365
\(11\) −1.00000 −0.301511
\(12\) −2.80122 −0.808641
\(13\) −2.65369 −0.736000 −0.368000 0.929826i \(-0.619957\pi\)
−0.368000 + 0.929826i \(0.619957\pi\)
\(14\) 4.95875 1.32528
\(15\) 0.350829 0.0905837
\(16\) 17.3364 4.33409
\(17\) −1.00000 −0.242536
\(18\) 7.67358 1.80868
\(19\) −1.91939 −0.440339 −0.220170 0.975462i \(-0.570661\pi\)
−0.220170 + 0.975462i \(0.570661\pi\)
\(20\) −4.10651 −0.918243
\(21\) 0.872723 0.190444
\(22\) 2.77959 0.592611
\(23\) 2.92463 0.609828 0.304914 0.952380i \(-0.401372\pi\)
0.304914 + 0.952380i \(0.401372\pi\)
\(24\) 5.06669 1.03423
\(25\) −4.48569 −0.897139
\(26\) 7.37616 1.44658
\(27\) 2.81812 0.542347
\(28\) −10.2153 −1.93052
\(29\) 3.37416 0.626565 0.313282 0.949660i \(-0.398571\pi\)
0.313282 + 0.949660i \(0.398571\pi\)
\(30\) −0.975163 −0.178040
\(31\) −2.56007 −0.459802 −0.229901 0.973214i \(-0.573840\pi\)
−0.229901 + 0.973214i \(0.573840\pi\)
\(32\) −27.4737 −4.85672
\(33\) 0.489198 0.0851585
\(34\) 2.77959 0.476696
\(35\) 1.27939 0.216256
\(36\) −15.8081 −2.63468
\(37\) 11.2450 1.84867 0.924334 0.381583i \(-0.124621\pi\)
0.924334 + 0.381583i \(0.124621\pi\)
\(38\) 5.33513 0.865473
\(39\) 1.29818 0.207875
\(40\) 7.42764 1.17441
\(41\) 4.76123 0.743579 0.371789 0.928317i \(-0.378744\pi\)
0.371789 + 0.928317i \(0.378744\pi\)
\(42\) −2.42581 −0.374311
\(43\) −1.00000 −0.152499
\(44\) −5.72614 −0.863247
\(45\) 1.97983 0.295136
\(46\) −8.12929 −1.19860
\(47\) −0.457282 −0.0667014 −0.0333507 0.999444i \(-0.510618\pi\)
−0.0333507 + 0.999444i \(0.510618\pi\)
\(48\) −8.48091 −1.22411
\(49\) −3.81739 −0.545342
\(50\) 12.4684 1.76330
\(51\) 0.489198 0.0685015
\(52\) −15.1954 −2.10722
\(53\) −5.27651 −0.724784 −0.362392 0.932026i \(-0.618040\pi\)
−0.362392 + 0.932026i \(0.618040\pi\)
\(54\) −7.83322 −1.06597
\(55\) 0.717152 0.0967007
\(56\) 18.4770 2.46909
\(57\) 0.938964 0.124369
\(58\) −9.37878 −1.23149
\(59\) −1.26303 −0.164432 −0.0822162 0.996615i \(-0.526200\pi\)
−0.0822162 + 0.996615i \(0.526200\pi\)
\(60\) 2.00890 0.259347
\(61\) −13.8801 −1.77717 −0.888585 0.458713i \(-0.848311\pi\)
−0.888585 + 0.458713i \(0.848311\pi\)
\(62\) 7.11595 0.903726
\(63\) 4.92502 0.620495
\(64\) 41.6931 5.21163
\(65\) 1.90309 0.236050
\(66\) −1.35977 −0.167376
\(67\) 13.3080 1.62583 0.812917 0.582380i \(-0.197879\pi\)
0.812917 + 0.582380i \(0.197879\pi\)
\(68\) −5.72614 −0.694396
\(69\) −1.43073 −0.172239
\(70\) −3.55618 −0.425045
\(71\) −0.440272 −0.0522507 −0.0261254 0.999659i \(-0.508317\pi\)
−0.0261254 + 0.999659i \(0.508317\pi\)
\(72\) 28.5928 3.36969
\(73\) 12.3438 1.44473 0.722364 0.691513i \(-0.243056\pi\)
0.722364 + 0.691513i \(0.243056\pi\)
\(74\) −31.2566 −3.63350
\(75\) 2.19439 0.253387
\(76\) −10.9907 −1.26072
\(77\) 1.78399 0.203304
\(78\) −3.60841 −0.408572
\(79\) 14.4491 1.62565 0.812823 0.582511i \(-0.197930\pi\)
0.812823 + 0.582511i \(0.197930\pi\)
\(80\) −12.4328 −1.39003
\(81\) 6.90344 0.767049
\(82\) −13.2343 −1.46148
\(83\) −2.65016 −0.290893 −0.145447 0.989366i \(-0.546462\pi\)
−0.145447 + 0.989366i \(0.546462\pi\)
\(84\) 4.99733 0.545253
\(85\) 0.717152 0.0777860
\(86\) 2.77959 0.299731
\(87\) −1.65063 −0.176966
\(88\) 10.3571 1.10407
\(89\) −16.2884 −1.72657 −0.863284 0.504718i \(-0.831597\pi\)
−0.863284 + 0.504718i \(0.831597\pi\)
\(90\) −5.50312 −0.580080
\(91\) 4.73414 0.496272
\(92\) 16.7469 1.74598
\(93\) 1.25238 0.129866
\(94\) 1.27106 0.131100
\(95\) 1.37650 0.141226
\(96\) 13.4401 1.37172
\(97\) 18.0088 1.82852 0.914258 0.405133i \(-0.132775\pi\)
0.914258 + 0.405133i \(0.132775\pi\)
\(98\) 10.6108 1.07185
\(99\) 2.76069 0.277459
\(100\) −25.6857 −2.56857
\(101\) −10.5009 −1.04488 −0.522439 0.852677i \(-0.674978\pi\)
−0.522439 + 0.852677i \(0.674978\pi\)
\(102\) −1.35977 −0.134637
\(103\) 17.7249 1.74649 0.873245 0.487282i \(-0.162012\pi\)
0.873245 + 0.487282i \(0.162012\pi\)
\(104\) 27.4846 2.69509
\(105\) −0.625875 −0.0610791
\(106\) 14.6665 1.42454
\(107\) 3.80869 0.368200 0.184100 0.982907i \(-0.441063\pi\)
0.184100 + 0.982907i \(0.441063\pi\)
\(108\) 16.1369 1.55278
\(109\) 5.32049 0.509610 0.254805 0.966992i \(-0.417989\pi\)
0.254805 + 0.966992i \(0.417989\pi\)
\(110\) −1.99339 −0.190062
\(111\) −5.50104 −0.522136
\(112\) −30.9278 −2.92240
\(113\) 9.54212 0.897647 0.448824 0.893620i \(-0.351843\pi\)
0.448824 + 0.893620i \(0.351843\pi\)
\(114\) −2.60994 −0.244443
\(115\) −2.09741 −0.195584
\(116\) 19.3209 1.79390
\(117\) 7.32599 0.677288
\(118\) 3.51071 0.323187
\(119\) 1.78399 0.163538
\(120\) −3.63359 −0.331700
\(121\) 1.00000 0.0909091
\(122\) 38.5811 3.49297
\(123\) −2.32918 −0.210015
\(124\) −14.6593 −1.31644
\(125\) 6.80268 0.608450
\(126\) −13.6896 −1.21956
\(127\) 15.1289 1.34247 0.671236 0.741244i \(-0.265764\pi\)
0.671236 + 0.741244i \(0.265764\pi\)
\(128\) −60.9423 −5.38659
\(129\) 0.489198 0.0430715
\(130\) −5.28983 −0.463949
\(131\) −5.60889 −0.490051 −0.245025 0.969517i \(-0.578796\pi\)
−0.245025 + 0.969517i \(0.578796\pi\)
\(132\) 2.80122 0.243814
\(133\) 3.42417 0.296913
\(134\) −36.9909 −3.19552
\(135\) −2.02102 −0.173941
\(136\) 10.3571 0.888117
\(137\) −2.41469 −0.206300 −0.103150 0.994666i \(-0.532892\pi\)
−0.103150 + 0.994666i \(0.532892\pi\)
\(138\) 3.97684 0.338531
\(139\) 2.64721 0.224533 0.112267 0.993678i \(-0.464189\pi\)
0.112267 + 0.993678i \(0.464189\pi\)
\(140\) 7.32595 0.619156
\(141\) 0.223702 0.0188391
\(142\) 1.22378 0.102697
\(143\) 2.65369 0.221912
\(144\) −47.8602 −3.98835
\(145\) −2.41978 −0.200952
\(146\) −34.3106 −2.83957
\(147\) 1.86746 0.154026
\(148\) 64.3905 5.29286
\(149\) −12.1443 −0.994897 −0.497448 0.867494i \(-0.665730\pi\)
−0.497448 + 0.867494i \(0.665730\pi\)
\(150\) −6.09952 −0.498024
\(151\) −14.1516 −1.15164 −0.575819 0.817577i \(-0.695317\pi\)
−0.575819 + 0.817577i \(0.695317\pi\)
\(152\) 19.8794 1.61243
\(153\) 2.76069 0.223188
\(154\) −4.95875 −0.399588
\(155\) 1.83596 0.147468
\(156\) 7.43354 0.595160
\(157\) −8.32117 −0.664102 −0.332051 0.943261i \(-0.607741\pi\)
−0.332051 + 0.943261i \(0.607741\pi\)
\(158\) −40.1625 −3.19516
\(159\) 2.58126 0.204707
\(160\) 19.7028 1.55765
\(161\) −5.21751 −0.411197
\(162\) −19.1887 −1.50761
\(163\) 17.4759 1.36882 0.684409 0.729098i \(-0.260060\pi\)
0.684409 + 0.729098i \(0.260060\pi\)
\(164\) 27.2634 2.12892
\(165\) −0.350829 −0.0273120
\(166\) 7.36637 0.571741
\(167\) −21.7669 −1.68437 −0.842187 0.539185i \(-0.818732\pi\)
−0.842187 + 0.539185i \(0.818732\pi\)
\(168\) −9.03891 −0.697367
\(169\) −5.95796 −0.458304
\(170\) −1.99339 −0.152886
\(171\) 5.29884 0.405213
\(172\) −5.72614 −0.436614
\(173\) 24.5890 1.86947 0.934734 0.355348i \(-0.115638\pi\)
0.934734 + 0.355348i \(0.115638\pi\)
\(174\) 4.58808 0.347822
\(175\) 8.00241 0.604926
\(176\) −17.3364 −1.30678
\(177\) 0.617872 0.0464421
\(178\) 45.2752 3.39352
\(179\) 13.5365 1.01176 0.505881 0.862603i \(-0.331167\pi\)
0.505881 + 0.862603i \(0.331167\pi\)
\(180\) 11.3368 0.844993
\(181\) 3.66616 0.272503 0.136252 0.990674i \(-0.456494\pi\)
0.136252 + 0.990674i \(0.456494\pi\)
\(182\) −13.1590 −0.975408
\(183\) 6.79014 0.501941
\(184\) −30.2908 −2.23307
\(185\) −8.06438 −0.592905
\(186\) −3.48111 −0.255247
\(187\) 1.00000 0.0731272
\(188\) −2.61846 −0.190971
\(189\) −5.02748 −0.365695
\(190\) −3.82610 −0.277574
\(191\) 16.5546 1.19785 0.598924 0.800806i \(-0.295595\pi\)
0.598924 + 0.800806i \(0.295595\pi\)
\(192\) −20.3962 −1.47197
\(193\) −15.4859 −1.11470 −0.557350 0.830278i \(-0.688182\pi\)
−0.557350 + 0.830278i \(0.688182\pi\)
\(194\) −50.0571 −3.59389
\(195\) −0.930990 −0.0666696
\(196\) −21.8589 −1.56135
\(197\) −1.46484 −0.104365 −0.0521826 0.998638i \(-0.516618\pi\)
−0.0521826 + 0.998638i \(0.516618\pi\)
\(198\) −7.67358 −0.545338
\(199\) −10.6094 −0.752080 −0.376040 0.926603i \(-0.622715\pi\)
−0.376040 + 0.926603i \(0.622715\pi\)
\(200\) 46.4590 3.28514
\(201\) −6.51026 −0.459198
\(202\) 29.1882 2.05367
\(203\) −6.01945 −0.422482
\(204\) 2.80122 0.196124
\(205\) −3.41452 −0.238480
\(206\) −49.2681 −3.43267
\(207\) −8.07400 −0.561181
\(208\) −46.0052 −3.18989
\(209\) 1.91939 0.132767
\(210\) 1.73968 0.120049
\(211\) −8.01027 −0.551450 −0.275725 0.961237i \(-0.588918\pi\)
−0.275725 + 0.961237i \(0.588918\pi\)
\(212\) −30.2140 −2.07511
\(213\) 0.215380 0.0147576
\(214\) −10.5866 −0.723686
\(215\) 0.717152 0.0489093
\(216\) −29.1876 −1.98597
\(217\) 4.56712 0.310037
\(218\) −14.7888 −1.00162
\(219\) −6.03854 −0.408047
\(220\) 4.10651 0.276861
\(221\) 2.65369 0.178506
\(222\) 15.2907 1.02624
\(223\) −11.3710 −0.761457 −0.380728 0.924687i \(-0.624327\pi\)
−0.380728 + 0.924687i \(0.624327\pi\)
\(224\) 49.0128 3.27480
\(225\) 12.3836 0.825572
\(226\) −26.5232 −1.76430
\(227\) −14.7188 −0.976922 −0.488461 0.872586i \(-0.662441\pi\)
−0.488461 + 0.872586i \(0.662441\pi\)
\(228\) 5.37664 0.356076
\(229\) 15.6185 1.03210 0.516050 0.856558i \(-0.327402\pi\)
0.516050 + 0.856558i \(0.327402\pi\)
\(230\) 5.82994 0.384415
\(231\) −0.872723 −0.0574209
\(232\) −34.9466 −2.29436
\(233\) −20.5061 −1.34340 −0.671700 0.740824i \(-0.734435\pi\)
−0.671700 + 0.740824i \(0.734435\pi\)
\(234\) −20.3633 −1.33119
\(235\) 0.327941 0.0213925
\(236\) −7.23228 −0.470781
\(237\) −7.06845 −0.459145
\(238\) −4.95875 −0.321428
\(239\) −27.1275 −1.75473 −0.877367 0.479819i \(-0.840702\pi\)
−0.877367 + 0.479819i \(0.840702\pi\)
\(240\) 6.08210 0.392598
\(241\) 19.5058 1.25648 0.628240 0.778020i \(-0.283776\pi\)
0.628240 + 0.778020i \(0.283776\pi\)
\(242\) −2.77959 −0.178679
\(243\) −11.8315 −0.758991
\(244\) −79.4795 −5.08816
\(245\) 2.73765 0.174902
\(246\) 6.47418 0.412779
\(247\) 5.09347 0.324090
\(248\) 26.5150 1.68370
\(249\) 1.29646 0.0821595
\(250\) −18.9087 −1.19589
\(251\) −11.4796 −0.724588 −0.362294 0.932064i \(-0.618006\pi\)
−0.362294 + 0.932064i \(0.618006\pi\)
\(252\) 28.2014 1.77652
\(253\) −2.92463 −0.183870
\(254\) −42.0521 −2.63859
\(255\) −0.350829 −0.0219698
\(256\) 86.0086 5.37554
\(257\) −10.9675 −0.684132 −0.342066 0.939676i \(-0.611127\pi\)
−0.342066 + 0.939676i \(0.611127\pi\)
\(258\) −1.35977 −0.0846557
\(259\) −20.0609 −1.24653
\(260\) 10.8974 0.675827
\(261\) −9.31498 −0.576583
\(262\) 15.5904 0.963180
\(263\) −14.5632 −0.898006 −0.449003 0.893530i \(-0.648221\pi\)
−0.449003 + 0.893530i \(0.648221\pi\)
\(264\) −5.06669 −0.311833
\(265\) 3.78406 0.232453
\(266\) −9.51780 −0.583574
\(267\) 7.96826 0.487650
\(268\) 76.2035 4.65487
\(269\) 21.0459 1.28319 0.641595 0.767044i \(-0.278273\pi\)
0.641595 + 0.767044i \(0.278273\pi\)
\(270\) 5.61760 0.341877
\(271\) −17.0256 −1.03423 −0.517117 0.855915i \(-0.672995\pi\)
−0.517117 + 0.855915i \(0.672995\pi\)
\(272\) −17.3364 −1.05117
\(273\) −2.31593 −0.140167
\(274\) 6.71184 0.405477
\(275\) 4.48569 0.270497
\(276\) −8.19253 −0.493132
\(277\) −7.33517 −0.440728 −0.220364 0.975418i \(-0.570724\pi\)
−0.220364 + 0.975418i \(0.570724\pi\)
\(278\) −7.35816 −0.441313
\(279\) 7.06754 0.423123
\(280\) −13.2508 −0.791887
\(281\) −5.45211 −0.325246 −0.162623 0.986688i \(-0.551995\pi\)
−0.162623 + 0.986688i \(0.551995\pi\)
\(282\) −0.621799 −0.0370276
\(283\) −9.33787 −0.555079 −0.277539 0.960714i \(-0.589519\pi\)
−0.277539 + 0.960714i \(0.589519\pi\)
\(284\) −2.52106 −0.149597
\(285\) −0.673380 −0.0398876
\(286\) −7.37616 −0.436162
\(287\) −8.49396 −0.501383
\(288\) 75.8463 4.46929
\(289\) 1.00000 0.0588235
\(290\) 6.72601 0.394965
\(291\) −8.80987 −0.516444
\(292\) 70.6820 4.13635
\(293\) 5.39843 0.315380 0.157690 0.987489i \(-0.449595\pi\)
0.157690 + 0.987489i \(0.449595\pi\)
\(294\) −5.19078 −0.302733
\(295\) 0.905783 0.0527368
\(296\) −116.466 −6.76946
\(297\) −2.81812 −0.163524
\(298\) 33.7561 1.95544
\(299\) −7.76106 −0.448834
\(300\) 12.5654 0.725463
\(301\) 1.78399 0.102827
\(302\) 39.3356 2.26351
\(303\) 5.13702 0.295114
\(304\) −33.2753 −1.90847
\(305\) 9.95416 0.569974
\(306\) −7.67358 −0.438669
\(307\) 23.0994 1.31835 0.659175 0.751989i \(-0.270906\pi\)
0.659175 + 0.751989i \(0.270906\pi\)
\(308\) 10.2153 0.582073
\(309\) −8.67100 −0.493276
\(310\) −5.10321 −0.289843
\(311\) 19.3785 1.09885 0.549426 0.835542i \(-0.314846\pi\)
0.549426 + 0.835542i \(0.314846\pi\)
\(312\) −13.4454 −0.761196
\(313\) 25.4255 1.43714 0.718568 0.695456i \(-0.244798\pi\)
0.718568 + 0.695456i \(0.244798\pi\)
\(314\) 23.1295 1.30527
\(315\) −3.53199 −0.199005
\(316\) 82.7373 4.65433
\(317\) −26.8607 −1.50865 −0.754324 0.656502i \(-0.772035\pi\)
−0.754324 + 0.656502i \(0.772035\pi\)
\(318\) −7.17484 −0.402345
\(319\) −3.37416 −0.188916
\(320\) −29.9003 −1.67148
\(321\) −1.86321 −0.103994
\(322\) 14.5025 0.808195
\(323\) 1.91939 0.106798
\(324\) 39.5300 2.19611
\(325\) 11.9036 0.660294
\(326\) −48.5759 −2.69037
\(327\) −2.60277 −0.143934
\(328\) −49.3127 −2.72284
\(329\) 0.815785 0.0449757
\(330\) 0.975163 0.0536809
\(331\) 5.04191 0.277129 0.138564 0.990353i \(-0.455751\pi\)
0.138564 + 0.990353i \(0.455751\pi\)
\(332\) −15.1752 −0.832847
\(333\) −31.0439 −1.70120
\(334\) 60.5032 3.31059
\(335\) −9.54387 −0.521437
\(336\) 15.1298 0.825400
\(337\) 22.4238 1.22150 0.610752 0.791822i \(-0.290867\pi\)
0.610752 + 0.791822i \(0.290867\pi\)
\(338\) 16.5607 0.900783
\(339\) −4.66799 −0.253530
\(340\) 4.10651 0.222707
\(341\) 2.56007 0.138635
\(342\) −14.7286 −0.796433
\(343\) 19.2981 1.04200
\(344\) 10.3571 0.558420
\(345\) 1.02605 0.0552405
\(346\) −68.3475 −3.67438
\(347\) 31.7997 1.70710 0.853548 0.521015i \(-0.174446\pi\)
0.853548 + 0.521015i \(0.174446\pi\)
\(348\) −9.45174 −0.506666
\(349\) 32.7078 1.75081 0.875404 0.483392i \(-0.160595\pi\)
0.875404 + 0.483392i \(0.160595\pi\)
\(350\) −22.2435 −1.18896
\(351\) −7.47839 −0.399167
\(352\) 27.4737 1.46435
\(353\) 1.49905 0.0797864 0.0398932 0.999204i \(-0.487298\pi\)
0.0398932 + 0.999204i \(0.487298\pi\)
\(354\) −1.71743 −0.0912804
\(355\) 0.315742 0.0167578
\(356\) −93.2697 −4.94328
\(357\) −0.872723 −0.0461894
\(358\) −37.6258 −1.98859
\(359\) −21.4632 −1.13279 −0.566393 0.824135i \(-0.691662\pi\)
−0.566393 + 0.824135i \(0.691662\pi\)
\(360\) −20.5054 −1.08073
\(361\) −15.3159 −0.806101
\(362\) −10.1904 −0.535597
\(363\) −0.489198 −0.0256762
\(364\) 27.1083 1.42086
\(365\) −8.85235 −0.463353
\(366\) −18.8738 −0.986550
\(367\) 11.9337 0.622937 0.311468 0.950257i \(-0.399179\pi\)
0.311468 + 0.950257i \(0.399179\pi\)
\(368\) 50.7025 2.64305
\(369\) −13.1442 −0.684262
\(370\) 22.4157 1.16534
\(371\) 9.41321 0.488710
\(372\) 7.17130 0.371815
\(373\) 16.7645 0.868033 0.434016 0.900905i \(-0.357096\pi\)
0.434016 + 0.900905i \(0.357096\pi\)
\(374\) −2.77959 −0.143729
\(375\) −3.32786 −0.171850
\(376\) 4.73613 0.244247
\(377\) −8.95395 −0.461152
\(378\) 13.9743 0.718763
\(379\) −16.0006 −0.821897 −0.410949 0.911659i \(-0.634802\pi\)
−0.410949 + 0.911659i \(0.634802\pi\)
\(380\) 7.88201 0.404338
\(381\) −7.40102 −0.379166
\(382\) −46.0150 −2.35433
\(383\) −15.7420 −0.804381 −0.402190 0.915556i \(-0.631751\pi\)
−0.402190 + 0.915556i \(0.631751\pi\)
\(384\) 29.8129 1.52138
\(385\) −1.27939 −0.0652037
\(386\) 43.0445 2.19091
\(387\) 2.76069 0.140334
\(388\) 103.121 5.23516
\(389\) −29.8938 −1.51567 −0.757837 0.652444i \(-0.773744\pi\)
−0.757837 + 0.652444i \(0.773744\pi\)
\(390\) 2.58777 0.131037
\(391\) −2.92463 −0.147905
\(392\) 39.5373 1.99693
\(393\) 2.74386 0.138409
\(394\) 4.07165 0.205127
\(395\) −10.3622 −0.521377
\(396\) 15.8081 0.794385
\(397\) 15.3964 0.772722 0.386361 0.922348i \(-0.373732\pi\)
0.386361 + 0.922348i \(0.373732\pi\)
\(398\) 29.4898 1.47819
\(399\) −1.67510 −0.0838598
\(400\) −77.7656 −3.88828
\(401\) 9.36974 0.467902 0.233951 0.972248i \(-0.424834\pi\)
0.233951 + 0.972248i \(0.424834\pi\)
\(402\) 18.0959 0.902540
\(403\) 6.79361 0.338414
\(404\) −60.1295 −2.99156
\(405\) −4.95081 −0.246008
\(406\) 16.7316 0.830376
\(407\) −11.2450 −0.557395
\(408\) −5.06669 −0.250839
\(409\) −8.89437 −0.439798 −0.219899 0.975523i \(-0.570573\pi\)
−0.219899 + 0.975523i \(0.570573\pi\)
\(410\) 9.49098 0.468726
\(411\) 1.18126 0.0582672
\(412\) 101.495 5.00032
\(413\) 2.25323 0.110874
\(414\) 22.4424 1.10298
\(415\) 1.90057 0.0932953
\(416\) 72.9066 3.57454
\(417\) −1.29501 −0.0634169
\(418\) −5.33513 −0.260950
\(419\) 3.13764 0.153284 0.0766419 0.997059i \(-0.475580\pi\)
0.0766419 + 0.997059i \(0.475580\pi\)
\(420\) −3.58384 −0.174874
\(421\) 11.8913 0.579549 0.289774 0.957095i \(-0.406420\pi\)
0.289774 + 0.957095i \(0.406420\pi\)
\(422\) 22.2653 1.08386
\(423\) 1.26241 0.0613806
\(424\) 54.6495 2.65401
\(425\) 4.48569 0.217588
\(426\) −0.598670 −0.0290056
\(427\) 24.7620 1.19832
\(428\) 21.8091 1.05418
\(429\) −1.29818 −0.0626766
\(430\) −1.99339 −0.0961298
\(431\) 9.04070 0.435475 0.217738 0.976007i \(-0.430132\pi\)
0.217738 + 0.976007i \(0.430132\pi\)
\(432\) 48.8559 2.35058
\(433\) −34.6003 −1.66278 −0.831392 0.555686i \(-0.812456\pi\)
−0.831392 + 0.555686i \(0.812456\pi\)
\(434\) −12.6947 −0.609367
\(435\) 1.18375 0.0567566
\(436\) 30.4658 1.45905
\(437\) −5.61353 −0.268531
\(438\) 16.7847 0.802004
\(439\) 24.2461 1.15720 0.578601 0.815610i \(-0.303599\pi\)
0.578601 + 0.815610i \(0.303599\pi\)
\(440\) −7.42764 −0.354099
\(441\) 10.5386 0.501839
\(442\) −7.37616 −0.350848
\(443\) −22.9778 −1.09171 −0.545855 0.837880i \(-0.683795\pi\)
−0.545855 + 0.837880i \(0.683795\pi\)
\(444\) −31.4997 −1.49491
\(445\) 11.6813 0.553745
\(446\) 31.6067 1.49662
\(447\) 5.94095 0.280997
\(448\) −74.3799 −3.51412
\(449\) −19.0000 −0.896665 −0.448332 0.893867i \(-0.647982\pi\)
−0.448332 + 0.893867i \(0.647982\pi\)
\(450\) −34.4213 −1.62264
\(451\) −4.76123 −0.224197
\(452\) 54.6395 2.57002
\(453\) 6.92292 0.325267
\(454\) 40.9123 1.92011
\(455\) −3.39509 −0.159164
\(456\) −9.72498 −0.455414
\(457\) 5.86527 0.274366 0.137183 0.990546i \(-0.456195\pi\)
0.137183 + 0.990546i \(0.456195\pi\)
\(458\) −43.4131 −2.02856
\(459\) −2.81812 −0.131538
\(460\) −12.0100 −0.559971
\(461\) 23.2379 1.08230 0.541148 0.840928i \(-0.317990\pi\)
0.541148 + 0.840928i \(0.317990\pi\)
\(462\) 2.42581 0.112859
\(463\) −31.9003 −1.48253 −0.741267 0.671210i \(-0.765775\pi\)
−0.741267 + 0.671210i \(0.765775\pi\)
\(464\) 58.4956 2.71559
\(465\) −0.898147 −0.0416506
\(466\) 56.9986 2.64041
\(467\) 11.8036 0.546203 0.273102 0.961985i \(-0.411950\pi\)
0.273102 + 0.961985i \(0.411950\pi\)
\(468\) 41.9496 1.93912
\(469\) −23.7413 −1.09627
\(470\) −0.911541 −0.0420463
\(471\) 4.07070 0.187568
\(472\) 13.0814 0.602119
\(473\) 1.00000 0.0459800
\(474\) 19.6474 0.902436
\(475\) 8.60981 0.395045
\(476\) 10.2153 0.468220
\(477\) 14.5668 0.666967
\(478\) 75.4035 3.44888
\(479\) 25.6936 1.17397 0.586985 0.809598i \(-0.300315\pi\)
0.586985 + 0.809598i \(0.300315\pi\)
\(480\) −9.63859 −0.439939
\(481\) −29.8407 −1.36062
\(482\) −54.2182 −2.46957
\(483\) 2.55239 0.116138
\(484\) 5.72614 0.260279
\(485\) −12.9150 −0.586441
\(486\) 32.8868 1.49177
\(487\) 18.7901 0.851460 0.425730 0.904850i \(-0.360017\pi\)
0.425730 + 0.904850i \(0.360017\pi\)
\(488\) 143.759 6.50764
\(489\) −8.54918 −0.386607
\(490\) −7.60955 −0.343765
\(491\) −0.735094 −0.0331743 −0.0165872 0.999862i \(-0.505280\pi\)
−0.0165872 + 0.999862i \(0.505280\pi\)
\(492\) −13.3372 −0.601288
\(493\) −3.37416 −0.151964
\(494\) −14.1578 −0.636988
\(495\) −1.97983 −0.0889867
\(496\) −44.3822 −1.99282
\(497\) 0.785440 0.0352318
\(498\) −3.60362 −0.161482
\(499\) −17.7973 −0.796714 −0.398357 0.917230i \(-0.630420\pi\)
−0.398357 + 0.917230i \(0.630420\pi\)
\(500\) 38.9531 1.74203
\(501\) 10.6483 0.475733
\(502\) 31.9087 1.42416
\(503\) 7.75317 0.345697 0.172848 0.984948i \(-0.444703\pi\)
0.172848 + 0.984948i \(0.444703\pi\)
\(504\) −51.0092 −2.27213
\(505\) 7.53073 0.335113
\(506\) 8.12929 0.361391
\(507\) 2.91462 0.129443
\(508\) 86.6301 3.84359
\(509\) 25.8806 1.14714 0.573569 0.819158i \(-0.305559\pi\)
0.573569 + 0.819158i \(0.305559\pi\)
\(510\) 0.975163 0.0431809
\(511\) −22.0211 −0.974156
\(512\) −117.184 −5.17886
\(513\) −5.40908 −0.238817
\(514\) 30.4851 1.34464
\(515\) −12.7115 −0.560134
\(516\) 2.80122 0.123317
\(517\) 0.457282 0.0201112
\(518\) 55.7613 2.45001
\(519\) −12.0289 −0.528010
\(520\) −19.7106 −0.864368
\(521\) 20.7652 0.909740 0.454870 0.890558i \(-0.349686\pi\)
0.454870 + 0.890558i \(0.349686\pi\)
\(522\) 25.8919 1.13326
\(523\) −21.2531 −0.929333 −0.464666 0.885486i \(-0.653826\pi\)
−0.464666 + 0.885486i \(0.653826\pi\)
\(524\) −32.1173 −1.40305
\(525\) −3.91477 −0.170854
\(526\) 40.4798 1.76500
\(527\) 2.56007 0.111518
\(528\) 8.48091 0.369084
\(529\) −14.4465 −0.628109
\(530\) −10.5181 −0.456878
\(531\) 3.48683 0.151315
\(532\) 19.6073 0.850083
\(533\) −12.6348 −0.547274
\(534\) −22.1485 −0.958461
\(535\) −2.73141 −0.118089
\(536\) −137.833 −5.95348
\(537\) −6.62201 −0.285761
\(538\) −58.4989 −2.52207
\(539\) 3.81739 0.164427
\(540\) −11.5726 −0.498006
\(541\) −23.3890 −1.00557 −0.502785 0.864412i \(-0.667691\pi\)
−0.502785 + 0.864412i \(0.667691\pi\)
\(542\) 47.3243 2.03275
\(543\) −1.79348 −0.0769655
\(544\) 27.4737 1.17793
\(545\) −3.81560 −0.163442
\(546\) 6.43735 0.275493
\(547\) −24.1858 −1.03411 −0.517054 0.855953i \(-0.672972\pi\)
−0.517054 + 0.855953i \(0.672972\pi\)
\(548\) −13.8268 −0.590652
\(549\) 38.3187 1.63540
\(550\) −12.4684 −0.531654
\(551\) −6.47633 −0.275901
\(552\) 14.8182 0.630706
\(553\) −25.7769 −1.09615
\(554\) 20.3888 0.866237
\(555\) 3.94508 0.167459
\(556\) 15.1583 0.642854
\(557\) −28.1891 −1.19441 −0.597205 0.802089i \(-0.703722\pi\)
−0.597205 + 0.802089i \(0.703722\pi\)
\(558\) −19.6449 −0.831634
\(559\) 2.65369 0.112239
\(560\) 22.1799 0.937273
\(561\) −0.489198 −0.0206540
\(562\) 15.1547 0.639261
\(563\) 21.4085 0.902260 0.451130 0.892458i \(-0.351021\pi\)
0.451130 + 0.892458i \(0.351021\pi\)
\(564\) 1.28095 0.0539375
\(565\) −6.84315 −0.287893
\(566\) 25.9555 1.09099
\(567\) −12.3156 −0.517208
\(568\) 4.55996 0.191332
\(569\) −36.9116 −1.54741 −0.773707 0.633544i \(-0.781600\pi\)
−0.773707 + 0.633544i \(0.781600\pi\)
\(570\) 1.87172 0.0783978
\(571\) −7.03740 −0.294506 −0.147253 0.989099i \(-0.547043\pi\)
−0.147253 + 0.989099i \(0.547043\pi\)
\(572\) 15.1954 0.635350
\(573\) −8.09847 −0.338319
\(574\) 23.6097 0.985452
\(575\) −13.1190 −0.547101
\(576\) −115.101 −4.79589
\(577\) 22.6065 0.941122 0.470561 0.882367i \(-0.344051\pi\)
0.470561 + 0.882367i \(0.344051\pi\)
\(578\) −2.77959 −0.115616
\(579\) 7.57567 0.314834
\(580\) −13.8560 −0.575339
\(581\) 4.72785 0.196144
\(582\) 24.4878 1.01505
\(583\) 5.27651 0.218531
\(584\) −127.846 −5.29031
\(585\) −5.25384 −0.217220
\(586\) −15.0054 −0.619869
\(587\) −15.9229 −0.657209 −0.328605 0.944468i \(-0.606578\pi\)
−0.328605 + 0.944468i \(0.606578\pi\)
\(588\) 10.6933 0.440986
\(589\) 4.91378 0.202469
\(590\) −2.51771 −0.103652
\(591\) 0.716595 0.0294768
\(592\) 194.948 8.01230
\(593\) 13.0791 0.537095 0.268548 0.963266i \(-0.413456\pi\)
0.268548 + 0.963266i \(0.413456\pi\)
\(594\) 7.83322 0.321401
\(595\) −1.27939 −0.0524498
\(596\) −69.5397 −2.84846
\(597\) 5.19010 0.212417
\(598\) 21.5726 0.882169
\(599\) 38.6057 1.57739 0.788693 0.614787i \(-0.210758\pi\)
0.788693 + 0.614787i \(0.210758\pi\)
\(600\) −22.7276 −0.927852
\(601\) −25.7237 −1.04929 −0.524645 0.851321i \(-0.675802\pi\)
−0.524645 + 0.851321i \(0.675802\pi\)
\(602\) −4.95875 −0.202104
\(603\) −36.7392 −1.49614
\(604\) −81.0337 −3.29722
\(605\) −0.717152 −0.0291564
\(606\) −14.2788 −0.580037
\(607\) −13.3941 −0.543648 −0.271824 0.962347i \(-0.587627\pi\)
−0.271824 + 0.962347i \(0.587627\pi\)
\(608\) 52.7329 2.13860
\(609\) 2.94470 0.119325
\(610\) −27.6685 −1.12027
\(611\) 1.21348 0.0490922
\(612\) 15.8081 0.639003
\(613\) −15.9231 −0.643130 −0.321565 0.946888i \(-0.604209\pi\)
−0.321565 + 0.946888i \(0.604209\pi\)
\(614\) −64.2068 −2.59118
\(615\) 1.67038 0.0673561
\(616\) −18.4770 −0.744459
\(617\) −2.60308 −0.104796 −0.0523981 0.998626i \(-0.516686\pi\)
−0.0523981 + 0.998626i \(0.516686\pi\)
\(618\) 24.1019 0.969519
\(619\) 26.8211 1.07803 0.539016 0.842296i \(-0.318796\pi\)
0.539016 + 0.842296i \(0.318796\pi\)
\(620\) 10.5129 0.422210
\(621\) 8.24196 0.330739
\(622\) −53.8643 −2.15976
\(623\) 29.0583 1.16420
\(624\) 22.5057 0.900948
\(625\) 17.5499 0.701997
\(626\) −70.6727 −2.82465
\(627\) −0.938964 −0.0374986
\(628\) −47.6481 −1.90137
\(629\) −11.2450 −0.448368
\(630\) 9.81749 0.391138
\(631\) −41.5197 −1.65287 −0.826437 0.563028i \(-0.809636\pi\)
−0.826437 + 0.563028i \(0.809636\pi\)
\(632\) −149.651 −5.95279
\(633\) 3.91861 0.155751
\(634\) 74.6618 2.96520
\(635\) −10.8497 −0.430557
\(636\) 14.7806 0.586090
\(637\) 10.1302 0.401372
\(638\) 9.37878 0.371309
\(639\) 1.21545 0.0480826
\(640\) 43.7049 1.72759
\(641\) −7.92205 −0.312902 −0.156451 0.987686i \(-0.550005\pi\)
−0.156451 + 0.987686i \(0.550005\pi\)
\(642\) 5.17895 0.204397
\(643\) −40.0234 −1.57837 −0.789185 0.614156i \(-0.789497\pi\)
−0.789185 + 0.614156i \(0.789497\pi\)
\(644\) −29.8762 −1.17729
\(645\) −0.350829 −0.0138139
\(646\) −5.33513 −0.209908
\(647\) 27.8331 1.09423 0.547116 0.837057i \(-0.315726\pi\)
0.547116 + 0.837057i \(0.315726\pi\)
\(648\) −71.4999 −2.80878
\(649\) 1.26303 0.0495782
\(650\) −33.0872 −1.29779
\(651\) −2.23423 −0.0875664
\(652\) 100.069 3.91902
\(653\) −31.0691 −1.21583 −0.607914 0.794003i \(-0.707994\pi\)
−0.607914 + 0.794003i \(0.707994\pi\)
\(654\) 7.23465 0.282897
\(655\) 4.02242 0.157169
\(656\) 82.5423 3.22274
\(657\) −34.0772 −1.32948
\(658\) −2.26755 −0.0883983
\(659\) −39.3045 −1.53109 −0.765544 0.643384i \(-0.777530\pi\)
−0.765544 + 0.643384i \(0.777530\pi\)
\(660\) −2.00890 −0.0781962
\(661\) −35.3330 −1.37429 −0.687147 0.726518i \(-0.741137\pi\)
−0.687147 + 0.726518i \(0.741137\pi\)
\(662\) −14.0145 −0.544688
\(663\) −1.29818 −0.0504171
\(664\) 27.4481 1.06519
\(665\) −2.45565 −0.0952261
\(666\) 86.2895 3.34365
\(667\) 9.86817 0.382097
\(668\) −124.640 −4.82248
\(669\) 5.56266 0.215065
\(670\) 26.5281 1.02487
\(671\) 13.8801 0.535837
\(672\) −23.9770 −0.924931
\(673\) 3.13616 0.120890 0.0604451 0.998172i \(-0.480748\pi\)
0.0604451 + 0.998172i \(0.480748\pi\)
\(674\) −62.3291 −2.40083
\(675\) −12.6412 −0.486560
\(676\) −34.1161 −1.31216
\(677\) −34.4738 −1.32494 −0.662468 0.749090i \(-0.730491\pi\)
−0.662468 + 0.749090i \(0.730491\pi\)
\(678\) 12.9751 0.498306
\(679\) −32.1274 −1.23294
\(680\) −7.42764 −0.284837
\(681\) 7.20042 0.275921
\(682\) −7.11595 −0.272484
\(683\) −9.09626 −0.348059 −0.174029 0.984740i \(-0.555679\pi\)
−0.174029 + 0.984740i \(0.555679\pi\)
\(684\) 30.3419 1.16015
\(685\) 1.73170 0.0661647
\(686\) −53.6408 −2.04802
\(687\) −7.64055 −0.291505
\(688\) −17.3364 −0.660942
\(689\) 14.0022 0.533441
\(690\) −2.85199 −0.108574
\(691\) 18.0093 0.685108 0.342554 0.939498i \(-0.388708\pi\)
0.342554 + 0.939498i \(0.388708\pi\)
\(692\) 140.800 5.35241
\(693\) −4.92502 −0.187086
\(694\) −88.3901 −3.35524
\(695\) −1.89845 −0.0720123
\(696\) 17.0958 0.648015
\(697\) −4.76123 −0.180344
\(698\) −90.9144 −3.44116
\(699\) 10.0315 0.379428
\(700\) 45.8229 1.73194
\(701\) 7.51648 0.283894 0.141947 0.989874i \(-0.454664\pi\)
0.141947 + 0.989874i \(0.454664\pi\)
\(702\) 20.7869 0.784551
\(703\) −21.5836 −0.814041
\(704\) −41.6931 −1.57137
\(705\) −0.160428 −0.00604207
\(706\) −4.16675 −0.156818
\(707\) 18.7334 0.704544
\(708\) 3.53802 0.132967
\(709\) −22.7340 −0.853793 −0.426896 0.904301i \(-0.640393\pi\)
−0.426896 + 0.904301i \(0.640393\pi\)
\(710\) −0.877634 −0.0329370
\(711\) −39.8893 −1.49597
\(712\) 168.701 6.32235
\(713\) −7.48726 −0.280400
\(714\) 2.42581 0.0907838
\(715\) −1.90309 −0.0711717
\(716\) 77.5116 2.89674
\(717\) 13.2707 0.495605
\(718\) 59.6590 2.22646
\(719\) 48.6196 1.81320 0.906602 0.421986i \(-0.138667\pi\)
0.906602 + 0.421986i \(0.138667\pi\)
\(720\) 34.3230 1.27914
\(721\) −31.6210 −1.17763
\(722\) 42.5720 1.58437
\(723\) −9.54221 −0.354879
\(724\) 20.9929 0.780196
\(725\) −15.1354 −0.562116
\(726\) 1.35977 0.0504659
\(727\) −18.8705 −0.699870 −0.349935 0.936774i \(-0.613796\pi\)
−0.349935 + 0.936774i \(0.613796\pi\)
\(728\) −49.0321 −1.81725
\(729\) −14.9224 −0.552680
\(730\) 24.6059 0.910706
\(731\) 1.00000 0.0369863
\(732\) 38.8812 1.43709
\(733\) 5.70688 0.210788 0.105394 0.994431i \(-0.466390\pi\)
0.105394 + 0.994431i \(0.466390\pi\)
\(734\) −33.1710 −1.22436
\(735\) −1.33925 −0.0493991
\(736\) −80.3506 −2.96176
\(737\) −13.3080 −0.490207
\(738\) 36.5356 1.34490
\(739\) −27.8976 −1.02623 −0.513116 0.858320i \(-0.671509\pi\)
−0.513116 + 0.858320i \(0.671509\pi\)
\(740\) −46.1777 −1.69753
\(741\) −2.49172 −0.0915355
\(742\) −26.1649 −0.960544
\(743\) −40.3694 −1.48101 −0.740506 0.672050i \(-0.765414\pi\)
−0.740506 + 0.672050i \(0.765414\pi\)
\(744\) −12.9711 −0.475543
\(745\) 8.70928 0.319083
\(746\) −46.5985 −1.70609
\(747\) 7.31627 0.267688
\(748\) 5.72614 0.209368
\(749\) −6.79465 −0.248271
\(750\) 9.25009 0.337766
\(751\) 24.3300 0.887814 0.443907 0.896073i \(-0.353592\pi\)
0.443907 + 0.896073i \(0.353592\pi\)
\(752\) −7.92760 −0.289090
\(753\) 5.61582 0.204652
\(754\) 24.8883 0.906379
\(755\) 10.1488 0.369353
\(756\) −28.7880 −1.04701
\(757\) −19.5391 −0.710161 −0.355080 0.934836i \(-0.615547\pi\)
−0.355080 + 0.934836i \(0.615547\pi\)
\(758\) 44.4752 1.61541
\(759\) 1.43073 0.0519321
\(760\) −14.2566 −0.517140
\(761\) 35.3505 1.28145 0.640727 0.767769i \(-0.278633\pi\)
0.640727 + 0.767769i \(0.278633\pi\)
\(762\) 20.5718 0.745239
\(763\) −9.49168 −0.343622
\(764\) 94.7938 3.42952
\(765\) −1.97983 −0.0715809
\(766\) 43.7565 1.58099
\(767\) 3.35168 0.121022
\(768\) −42.0753 −1.51826
\(769\) −9.98347 −0.360013 −0.180007 0.983665i \(-0.557612\pi\)
−0.180007 + 0.983665i \(0.557612\pi\)
\(770\) 3.55618 0.128156
\(771\) 5.36527 0.193225
\(772\) −88.6744 −3.19146
\(773\) 29.4307 1.05855 0.529274 0.848451i \(-0.322464\pi\)
0.529274 + 0.848451i \(0.322464\pi\)
\(774\) −7.67358 −0.275821
\(775\) 11.4837 0.412506
\(776\) −186.520 −6.69566
\(777\) 9.81378 0.352067
\(778\) 83.0925 2.97901
\(779\) −9.13867 −0.327427
\(780\) −5.33098 −0.190880
\(781\) 0.440272 0.0157542
\(782\) 8.12929 0.290703
\(783\) 9.50876 0.339816
\(784\) −66.1797 −2.36356
\(785\) 5.96754 0.212991
\(786\) −7.62681 −0.272039
\(787\) −19.1425 −0.682357 −0.341179 0.939998i \(-0.610826\pi\)
−0.341179 + 0.939998i \(0.610826\pi\)
\(788\) −8.38785 −0.298805
\(789\) 7.12430 0.253632
\(790\) 28.8026 1.02475
\(791\) −17.0230 −0.605268
\(792\) −28.5928 −1.01600
\(793\) 36.8335 1.30800
\(794\) −42.7957 −1.51876
\(795\) −1.85115 −0.0656536
\(796\) −60.7509 −2.15326
\(797\) 25.0016 0.885604 0.442802 0.896620i \(-0.353985\pi\)
0.442802 + 0.896620i \(0.353985\pi\)
\(798\) 4.65609 0.164824
\(799\) 0.457282 0.0161775
\(800\) 123.239 4.35715
\(801\) 44.9672 1.58884
\(802\) −26.0441 −0.919648
\(803\) −12.3438 −0.435602
\(804\) −37.2786 −1.31472
\(805\) 3.74174 0.131879
\(806\) −18.8835 −0.665142
\(807\) −10.2956 −0.362422
\(808\) 108.759 3.82614
\(809\) 48.9099 1.71958 0.859790 0.510648i \(-0.170594\pi\)
0.859790 + 0.510648i \(0.170594\pi\)
\(810\) 13.7612 0.483521
\(811\) −32.1108 −1.12756 −0.563781 0.825924i \(-0.690654\pi\)
−0.563781 + 0.825924i \(0.690654\pi\)
\(812\) −34.4682 −1.20960
\(813\) 8.32891 0.292108
\(814\) 31.2566 1.09554
\(815\) −12.5329 −0.439007
\(816\) 8.48091 0.296891
\(817\) 1.91939 0.0671511
\(818\) 24.7227 0.864409
\(819\) −13.0695 −0.456684
\(820\) −19.5520 −0.682786
\(821\) −17.1261 −0.597704 −0.298852 0.954299i \(-0.596604\pi\)
−0.298852 + 0.954299i \(0.596604\pi\)
\(822\) −3.28342 −0.114522
\(823\) −16.1851 −0.564176 −0.282088 0.959389i \(-0.591027\pi\)
−0.282088 + 0.959389i \(0.591027\pi\)
\(824\) −183.580 −6.39530
\(825\) −2.19439 −0.0763990
\(826\) −6.26305 −0.217919
\(827\) 46.5392 1.61833 0.809163 0.587584i \(-0.199921\pi\)
0.809163 + 0.587584i \(0.199921\pi\)
\(828\) −46.2328 −1.60670
\(829\) 39.8359 1.38356 0.691778 0.722110i \(-0.256828\pi\)
0.691778 + 0.722110i \(0.256828\pi\)
\(830\) −5.28281 −0.183369
\(831\) 3.58835 0.124479
\(832\) −110.640 −3.83576
\(833\) 3.81739 0.132265
\(834\) 3.59960 0.124644
\(835\) 15.6102 0.540213
\(836\) 10.9907 0.380122
\(837\) −7.21457 −0.249372
\(838\) −8.72136 −0.301275
\(839\) −15.0363 −0.519110 −0.259555 0.965728i \(-0.583576\pi\)
−0.259555 + 0.965728i \(0.583576\pi\)
\(840\) 6.48227 0.223660
\(841\) −17.6151 −0.607416
\(842\) −33.0531 −1.13909
\(843\) 2.66716 0.0918620
\(844\) −45.8679 −1.57884
\(845\) 4.27276 0.146987
\(846\) −3.50899 −0.120642
\(847\) −1.78399 −0.0612985
\(848\) −91.4754 −3.14128
\(849\) 4.56807 0.156776
\(850\) −12.4684 −0.427663
\(851\) 32.8876 1.12737
\(852\) 1.23330 0.0422521
\(853\) −1.78880 −0.0612473 −0.0306237 0.999531i \(-0.509749\pi\)
−0.0306237 + 0.999531i \(0.509749\pi\)
\(854\) −68.8282 −2.35525
\(855\) −3.80007 −0.129960
\(856\) −39.4472 −1.34828
\(857\) 15.7528 0.538105 0.269052 0.963126i \(-0.413290\pi\)
0.269052 + 0.963126i \(0.413290\pi\)
\(858\) 3.60841 0.123189
\(859\) 17.9930 0.613912 0.306956 0.951724i \(-0.400690\pi\)
0.306956 + 0.951724i \(0.400690\pi\)
\(860\) 4.10651 0.140031
\(861\) 4.15523 0.141610
\(862\) −25.1295 −0.855913
\(863\) 9.28236 0.315975 0.157988 0.987441i \(-0.449499\pi\)
0.157988 + 0.987441i \(0.449499\pi\)
\(864\) −77.4242 −2.63402
\(865\) −17.6341 −0.599576
\(866\) 96.1747 3.26815
\(867\) −0.489198 −0.0166140
\(868\) 26.1520 0.887656
\(869\) −14.4491 −0.490151
\(870\) −3.29035 −0.111553
\(871\) −35.3153 −1.19661
\(872\) −55.1050 −1.86609
\(873\) −49.7166 −1.68265
\(874\) 15.6033 0.527790
\(875\) −12.1359 −0.410268
\(876\) −34.5775 −1.16827
\(877\) −40.7755 −1.37689 −0.688446 0.725287i \(-0.741707\pi\)
−0.688446 + 0.725287i \(0.741707\pi\)
\(878\) −67.3943 −2.27445
\(879\) −2.64090 −0.0890755
\(880\) 12.4328 0.419109
\(881\) 38.0087 1.28054 0.640272 0.768148i \(-0.278822\pi\)
0.640272 + 0.768148i \(0.278822\pi\)
\(882\) −29.2931 −0.986349
\(883\) 16.1164 0.542360 0.271180 0.962529i \(-0.412586\pi\)
0.271180 + 0.962529i \(0.412586\pi\)
\(884\) 15.1954 0.511075
\(885\) −0.443108 −0.0148949
\(886\) 63.8690 2.14572
\(887\) 1.51048 0.0507171 0.0253586 0.999678i \(-0.491927\pi\)
0.0253586 + 0.999678i \(0.491927\pi\)
\(888\) 56.9750 1.91196
\(889\) −26.9897 −0.905206
\(890\) −32.4692 −1.08837
\(891\) −6.90344 −0.231274
\(892\) −65.1117 −2.18010
\(893\) 0.877705 0.0293713
\(894\) −16.5134 −0.552292
\(895\) −9.70769 −0.324492
\(896\) 108.720 3.63209
\(897\) 3.79670 0.126768
\(898\) 52.8122 1.76237
\(899\) −8.63807 −0.288096
\(900\) 70.9101 2.36367
\(901\) 5.27651 0.175786
\(902\) 13.2343 0.440653
\(903\) −0.872723 −0.0290424
\(904\) −98.8291 −3.28701
\(905\) −2.62919 −0.0873973
\(906\) −19.2429 −0.639302
\(907\) 1.89086 0.0627850 0.0313925 0.999507i \(-0.490006\pi\)
0.0313925 + 0.999507i \(0.490006\pi\)
\(908\) −84.2819 −2.79699
\(909\) 28.9897 0.961526
\(910\) 9.43698 0.312833
\(911\) 45.9887 1.52367 0.761837 0.647769i \(-0.224298\pi\)
0.761837 + 0.647769i \(0.224298\pi\)
\(912\) 16.2782 0.539026
\(913\) 2.65016 0.0877076
\(914\) −16.3031 −0.539257
\(915\) −4.86956 −0.160983
\(916\) 89.4337 2.95497
\(917\) 10.0062 0.330433
\(918\) 7.83322 0.258535
\(919\) 32.8636 1.08407 0.542035 0.840356i \(-0.317654\pi\)
0.542035 + 0.840356i \(0.317654\pi\)
\(920\) 21.7231 0.716190
\(921\) −11.3002 −0.372353
\(922\) −64.5918 −2.12722
\(923\) 1.16834 0.0384565
\(924\) −4.99733 −0.164400
\(925\) −50.4417 −1.65851
\(926\) 88.6699 2.91388
\(927\) −48.9329 −1.60717
\(928\) −92.7006 −3.04305
\(929\) −12.3825 −0.406258 −0.203129 0.979152i \(-0.565111\pi\)
−0.203129 + 0.979152i \(0.565111\pi\)
\(930\) 2.49648 0.0818629
\(931\) 7.32708 0.240136
\(932\) −117.421 −3.84624
\(933\) −9.47992 −0.310359
\(934\) −32.8091 −1.07355
\(935\) −0.717152 −0.0234534
\(936\) −75.8763 −2.48009
\(937\) −33.0716 −1.08040 −0.540201 0.841536i \(-0.681652\pi\)
−0.540201 + 0.841536i \(0.681652\pi\)
\(938\) 65.9912 2.15469
\(939\) −12.4381 −0.405903
\(940\) 1.87783 0.0612481
\(941\) 26.2525 0.855807 0.427903 0.903824i \(-0.359252\pi\)
0.427903 + 0.903824i \(0.359252\pi\)
\(942\) −11.3149 −0.368659
\(943\) 13.9248 0.453455
\(944\) −21.8963 −0.712665
\(945\) 3.60547 0.117286
\(946\) −2.77959 −0.0903724
\(947\) 2.26808 0.0737026 0.0368513 0.999321i \(-0.488267\pi\)
0.0368513 + 0.999321i \(0.488267\pi\)
\(948\) −40.4749 −1.31456
\(949\) −32.7564 −1.06332
\(950\) −23.9318 −0.776449
\(951\) 13.1402 0.426101
\(952\) −18.4770 −0.598843
\(953\) −49.8224 −1.61391 −0.806953 0.590615i \(-0.798885\pi\)
−0.806953 + 0.590615i \(0.798885\pi\)
\(954\) −40.4897 −1.31090
\(955\) −11.8721 −0.384174
\(956\) −155.336 −5.02392
\(957\) 1.65063 0.0533573
\(958\) −71.4177 −2.30740
\(959\) 4.30776 0.139105
\(960\) 14.6272 0.472089
\(961\) −24.4461 −0.788582
\(962\) 82.9451 2.67426
\(963\) −10.5146 −0.338828
\(964\) 111.693 3.59739
\(965\) 11.1057 0.357506
\(966\) −7.09462 −0.228266
\(967\) −35.5401 −1.14289 −0.571446 0.820639i \(-0.693617\pi\)
−0.571446 + 0.820639i \(0.693617\pi\)
\(968\) −10.3571 −0.332891
\(969\) −0.938964 −0.0301639
\(970\) 35.8985 1.15263
\(971\) 20.1539 0.646770 0.323385 0.946267i \(-0.395179\pi\)
0.323385 + 0.946267i \(0.395179\pi\)
\(972\) −67.7488 −2.17304
\(973\) −4.72258 −0.151399
\(974\) −52.2288 −1.67352
\(975\) −5.82323 −0.186493
\(976\) −240.631 −7.70241
\(977\) −16.2581 −0.520143 −0.260071 0.965589i \(-0.583746\pi\)
−0.260071 + 0.965589i \(0.583746\pi\)
\(978\) 23.7632 0.759864
\(979\) 16.2884 0.520580
\(980\) 15.6762 0.500756
\(981\) −14.6882 −0.468958
\(982\) 2.04326 0.0652031
\(983\) 8.37311 0.267061 0.133530 0.991045i \(-0.457369\pi\)
0.133530 + 0.991045i \(0.457369\pi\)
\(984\) 24.1237 0.769035
\(985\) 1.05051 0.0334720
\(986\) 9.37878 0.298681
\(987\) −0.399080 −0.0127029
\(988\) 29.1659 0.927890
\(989\) −2.92463 −0.0929980
\(990\) 5.50312 0.174901
\(991\) 46.4511 1.47557 0.737783 0.675037i \(-0.235873\pi\)
0.737783 + 0.675037i \(0.235873\pi\)
\(992\) 70.3346 2.23313
\(993\) −2.46650 −0.0782719
\(994\) −2.18320 −0.0692470
\(995\) 7.60855 0.241207
\(996\) 7.42368 0.235228
\(997\) −41.5361 −1.31546 −0.657730 0.753254i \(-0.728483\pi\)
−0.657730 + 0.753254i \(0.728483\pi\)
\(998\) 49.4691 1.56592
\(999\) 31.6898 1.00262
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8041.2.a.h.1.1 74
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8041.2.a.h.1.1 74 1.1 even 1 trivial